A Formalization of Sequential, Parallel, and Continuous Rewriting

sequential rewriting, parallel rewriting, continuous rewriting, selective substitution grammars, context sensitive languages, recursively enumerable languages

A formalization of the sequential, parallel, and continuous rewriting based on a uniform underlying concept of selective substitution grammars is presented. Each of the rewriting modes is formalized through a universal derivation restriction characterizing the rewriting in question. It is shown that whichever of the three rewriting modes is formalized, the resulting grammars generate precisely the family of context sensitive languages. Moreover, when erasing productions are allowed, these grammars generate all recursively enumerable languages.

A formalization of the sequential, parallel, and continuous rewriting based on a uniform underlying concept of selective substitution grammars is presented. Each of the rewriting modes is formalized through a universal derivation restriction characterizing the rewriting in question. It is shown that whichever of the three rewriting modes is formalized, the resulting grammars generate precisely the family of context sensitive languages. Moreover, when erasing productions are allowed, these grammars generate all recursively enumerable languages.